There are a total of 76 teachers and students watching a school play. There are 4 teachers and 40 girls.
Write the ratio of boys to girls in lowest terms.

Given:

The height of the triangular prism is 15 cm.

The side lengths of the base are 3 cm, 4 cm and 5 cm.

To find:

The lateral surface area of the prism.

Solution:

The lateral surface area of the prism is:

[tex]LSA=Ph[/tex]

Where, P is the perimeter of base and h is the height of the prism.

We know that the perimeter of base is the sum of all sides of the base.

The perimeter of the prism is (3+4+5) cm and the height of the prism is 15 cm.

So, the lateral surface area of the prism is:

[tex]LSA=(3+4+5)\times 15[/tex]

[tex]LSA=(12)\times 15[/tex]

[tex]LSA=180[/tex]

Therefore, the lateral surface area of the prism is 180 square cm.

Answer:

New avaerage if 2 students (15 year old) left = 13

Step-by-step explanation:

Given:

Average age of 20 students = 13.2

Find:

New avaerage if 2 students (15 year old) left

Computtaion:

Sum of all 20 student's age = 20 x 13.2

Sum of all 20 student's age = 264

Sum of current 18 student's age = 264 - 15 - 15

Sum of current 18 student's age = 234

New avaerage if 2 students (15 year old) left = 234 / 18

New avaerage if 2 students (15 year old) left = 13

Answer:

so this is the correct answer right

Answer:

[tex]\frac{39}{8}[/tex]

Step-by-step explanation:

Multiply the numerators: [tex]13*3= 39[/tex]

Multiply the denominators: [tex]4*2=8[/tex]

Final answer: [tex]\frac{39}{8}[/tex]

It is in simplest form, by the way.

Answer:

x = 3.75

Step-by-step explanation:

-4x + 2 = -13

-4x = -13 - 2

-4x = -15

x = 3.75

Answer:

-13

Step-by-step explanation:

just think about it

Answer:

20.25

Step-by-step explanation:

21-3/4=20.25

Answer:

Step-by-step explanation:

a+b=21

a=21-b

b=3/4*a

b=3/4*(21-b)

b=3(21-b)/4

b=63-3b/4

4*b=63-3b

4b+3b=63

7b=63

b=63/7

b=9

Answer:

Find the are

Step-by-step explanation:

pi method

Answer:

$318

Step-by-step explanation:

Calculation to determine the predicted end-of-year value of a portfolio

Given expression 1.08s + 1.02b

Now let determine the Predicted end-of-year value

Predicted end-of-year value=1.08(200) +1.02(100)

Predicted end-of-year value=216+102

Predicted end-of-year value=$318

Therefore the predicted end-of-year value of a portfolio will be $318

Answer:

-50x+40

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

calculator

Answer:

RS = 19

Step-by-step explanation:

Given a segment joining the midpoints of 2 sides of a triangle then it is half the length of the third side, that is

- 5x + 44 = [tex]\frac{1}{2}[/tex] (18 + 4x) ( multiply both sides by 2 to clear the fraction )

- 10x + 88 = 18 + 4x ( add 10x to both sides )

88 = 18 + 14x ( subtract 18 from both sides )

70 = 14x ( divide both sides by 14 )

5 = x

Then

RS = - 5x + 44 = - 5(5) + 44 = - 25 + 44 = 19

Answer:

62 degrees

Step-by-step explanation:

Every triangle needs to have 180 degrees. Simply you have to add 60+58 which is 118 degrees. Then you subtract 180-118 which equals to 62 degrees.

Answer:

Capacity of Matti's green house = 367.5 cubic feet

Step-by-step explanation:

Given:

Base Width and Length = 7 feet by 15 feet

Height of prism = 7 feet

Find:

Capacity of Matti's green house

Computation:

Capacity of Matti's green house = Volume of rectangular base[triangular prism]

Volume of rectangular base[triangular prism] = Area of triangular base x Height

Capacity of Matti's green house = [(1/2)(7)(7)][15]

Capacity of Matti's green house = [(1/2)(49)][15]

Capacity of Matti's green house = [(24.5)][15]

Capacity of Matti's green house = 367.5 cubic feet

Answer:

367.5 Cubic ft3

Step-by-step explanation:

Just look at the other persons explanation

(Please give them brainliest)

Answer:

When you fold the number line ( vertically through the point zero on the number line ) you have successfully divided the number line into 2 equal halves.

Step-by-step explanation:

When you fold the number line ( vertically through the point zero on the number line ) you have successfully divided the number line into 2 equal halves. and this causes the points labelled on either side of the number line  to match up with with the points on the opposite side

They have equal lengths is the correct answer

Answer:

x=2

Step-by-step explanation:

Hi there!

Whenever we're solving an algebraic equation, our goal is always to isolate the variable, which in this case is x. We would do this by performing inverse operations on both sides of the equal sign to cancel values out.

[tex]10-2x + 3 = 5x-9 + 4x[/tex]

Combine like terms on both sides of the equal sign

[tex]10+ 3-2x = 5x+ 4x-9 \\13-2x = 9x-9[/tex]

Add 2x to both sides to cancel out -2x (addition is the inverse of subtraction)

[tex]13-2x +2x = 9x-9 +2x\\13 = 11x-9[/tex]

Add 9 to both sides to cancel out -9 and isolate 11x (addition is the inverse of subtraction)

[tex]13+9 = 11x-9+9\\22=11x[/tex]

Divide both sides by 11 to isolate x (division is the inverse of multiplication)[tex]\frac{22}{11} =\frac{11x}{11} \\2=x[/tex]

Therefore, x=2.

I hope this helps!

Answer:

I think the answer is 112.098 yards

Answer:

112 yards

It's 112.098, but the question says "about _____ yards", so I'd round it.

Step-by-step explanation:

Circumference is calculated by (2)(pi)(radius) or (pi)(diameter). We'll use the second one, since they gave you the diameter.

C = (pi)(diameter)

C = (3.14)(35.7)

C =112.098

Answer: [tex]n>14[/tex]

Step-by-step explanation:

Given

Misty needs to gather at least 20 flags for the parade

She has already gathered 6 flags

Inequality to find the number of flags needed is

[tex]n+6>20[/tex]

Subtract -6 from both sides

[tex]\Rightarrow n+6-6>20-6\\\Rightarrow n>14[/tex]

Therefore, option (j) is correct.

Answer:

28°

Step-by-step explanation:

Supplementary angles sum to 180°

( dozen sixes) + 80

= 12 × 6 + 80

= 72 + 80

= 152°

supplement = 180° - 152° = 28°

Step-by-step explanation:

I used Pythagoras Theorem to find the diagonal distance as placement of objects is right angles triangle.

[tex] {c}^{2} = {a}^{2} + {b}^{2} [/tex]

a : Elm street

b : Birch street

c : Diagonal distance

c^2 = a^2 + b^2

c^2 = 15^2 + 8^2

c^2 = 225 + 64

c = √289

c = 17 blocks

I added the total distance of the original route Joline took

= 15 blocks + 8 blocks

= 23 blocks

How much less distance does she have to walk if she took the diagonal route

= Total distance of original route - distance of diagonal route

= 23 - 17

= 6 blocks

Joline have to walk less 6 blocks if she took the diagonal route compared to her original route

Answer:

19.5 dollars

Step-by-step explanation:

9.75% of 200 is 19.5

Answer:

The Richter scale and how it measures earthquake magnitude. The Richter scale calculates an earthquake's magnitude (size) from the amplitude of the earthquake's largest seismic wave recorded by a seismograph. ... (That is, an earthquake measuring 5.0 releases 31 times more energy than an earthquake measuring 4.0.)

Answer:

It's

Step-by-step explanation:

4:45am. That's the correct answer

15 minutes before 5 in the morning is written as 4:45am

Answer:

The total volume of the apartment is

✔ 2,160

An hourly rating of 2.5 BTUs per cubic foot is required, so

✔ multiply the total volume by 2.5

Arthur needs an air conditioner that will provide

✔ 5,400

BTUs to properly cool his apartment.

Step-by-step explanation:

you're welcome

Answer:

2,160

multiply the total volume by 2.5

5,400 BTUs

Step-by-step explanation:

cause said so

Answer:

the probability is 2/3

Step-by-step explanation:

you want to divide 8 by 12

Answer:

47

Step-by-step explanation:

The missing angle is complementary to the angle shown and together they from 90.

Your missing angle is 90 - 43

Answer:

76 m²

Step-by-step explanation:

The figure has been decomposed into 3 rectangles as shown in the attachment. Therefore:

Area of the figure = area of rectangle 1 + area of rectangle 2 + area of rectangle 3

✔️Area of rectangle 1:

Area = L*W

L = 2 m

W = 4 m

Area = 2*4 = 8 m²

✔️Area of rectangle 2:

Area = L*W

L = 4 m

W = 6 - 4 = 2 m

Area = 4*2 = 8 m²

✔️Area of rectangle 3:

Area = L*W

L = 10 m

W = 6 m

Area = 10*6 = 60 m²

✅Area of the figure = 8 + 8 + 60

= 76 m²

Answer:

x=67

y=40

The angles equal 63 and 117

Step-by-step explanation:

88% sure

Answer:

option D : 130°

Step-by-step explanation:

m∠2 = m∠7 = 130° , (corresponding angles)

Answer:

Step-by-step explanation:

Use SOH CAH TOA to recall how the trig functions fit on a triangle

SOH: Sin(Ф)= Opp / Hyp

CAH: Cos(Ф)= Adj / Hyp

TOA: Tan(Ф) = Opp / Adj

copy the above onto your computer for future reference

sin(g) = 420/427

tan(z) = 77/420

cos(z) = 420/427

sin(m) = 427/427

part (E)   the sin of any right angle will be  1   :)

Answer:

Solution given:

Sin G=opposite/hypotenuse=420/427

TanZ=Opposite/adjacent=77/420

CosZ=adjacent/hypotenuse=420/427

Sin M=opposite/hypotenuse=427/427=1

Answer:

x = 21

Step-by-step explanation:

For a pentagon, n = 5.

Each angle measures:

(n - 2)180/5 = (5 - 2)(180)/5 = 108

5x + 3 = 108

5x = 105

x = 21